We have considered a few types of interaction between the particles, and out of all, we find that the lubrication interaction plays a vital role, particularly when the particles are confined in a channel which is the case in the current study (details not shown).
Therefore, we consider the lubrication interaction to study the rectification of particles.
The short range interaction force on a particle \(i\)  due to its neighbors reads [1]}, [2]},
\(\displaystyle { \vec{F}_\mathrm {int} = \sum _{ j = 1, ~j \ne i}^{n} \frac{\sigma _{ij}}{d_{ij}}\left( \cos \theta _{ij}\, \hat{x} + \sin \theta _{ij} \, \hat{y} \right)},\) 
